50(1-1/102^5)+100/102^5 eching

$$50 ( 1 - \frac { 1 } { 102 ^ { 5 } } ) + \frac { 100 } { 102 ^ { 5 } }$$

Baholash

$$\frac{276020200825}{5520404016}\approx 50,000000005$$

Yechim qadamlari

5 daraja ko‘rsatkichini 102 ga hisoblang va 11040808032 ni qiymatni oling.

$$50\left(1-\frac{1}{11040808032}\right)+\frac{100}{102^{5}}$$

1 ni \frac{11040808032}{11040808032} kasrga o‘giring.

$$50\left(\frac{11040808032}{11040808032}-\frac{1}{11040808032}\right)+\frac{100}{102^{5}}$$

\frac{11040808032}{11040808032} va \frac{1}{11040808032} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$50\times \frac{11040808032-1}{11040808032}+\frac{100}{102^{5}}$$

11040808031 olish uchun 11040808032 dan 1 ni ayirish.

$$50\times \frac{11040808031}{11040808032}+\frac{100}{102^{5}}$$

50\times \frac{11040808031}{11040808032} ni yagona kasrga aylantiring.

$$\frac{50\times 11040808031}{11040808032}+\frac{100}{102^{5}}$$

552040401550 hosil qilish uchun 50 va 11040808031 ni ko'paytirish.

$$\frac{552040401550}{11040808032}+\frac{100}{102^{5}}$$

\frac{552040401550}{11040808032} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{276020200775}{5520404016}+\frac{100}{102^{5}}$$

5 daraja ko‘rsatkichini 102 ga hisoblang va 11040808032 ni qiymatni oling.

$$\frac{276020200775}{5520404016}+\frac{100}{11040808032}$$

\frac{100}{11040808032} ulushini 4 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{276020200775}{5520404016}+\frac{25}{2760202008}$$

5520404016 va 2760202008 ning eng kichik umumiy karralisi 5520404016 ga teng. \frac{276020200775}{5520404016} va \frac{25}{2760202008} ni 5520404016 maxraj bilan kasrlarga aylantirib oling.

$$\frac{276020200775}{5520404016}+\frac{50}{5520404016}$$

\frac{276020200775}{5520404016} va \frac{50}{5520404016} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{276020200775+50}{5520404016}$$

276020200825 olish uchun 276020200775 va 50'ni qo'shing.

$$\frac{276020200825}{5520404016}$$

Omil

$$\frac{5 ^ {2} \cdot 61 \cdot 103 \cdot 251 \cdot 7001}{2 ^ {4} \cdot 3 ^ {5} \cdot 17 ^ {5}} = 50\frac{25}{5520404016} = 50,00000000452865$$